Index of content:
Volume 22, Issue 9, September 1995

The relaxation of supercoiled DNA molecules as a biophysical dosimeter for ionizing radiations: A feasibility study
View Description Hide DescriptionIn this paper we explore the feasibility of using DNA molecules as a biophysical radiation dosimeter. Supercoiled φX174 bacteriophage DNA molecules were irradiated with different gamma radiation doses. The strand breakage produced by ionizing radiation within supercoiled double‐stranded DNA molecules (RFI) yields relaxed circular DNA molecules (RFII) and linear DNA molecules (RFIII) as a result of single‐strand breaks and double‐strand breaks, respectively. The irradiated samples were subjected to electrophoresis on agarose gels to separate the three forms. A proprietary fluorescent dye was used to detect DNA bands within the gel, which was photographed under UVtransillumination. The negative was scanned with a computerized imaging densitometric system for DNA band quantitation. The relative fractions of the three molecular forms are dose dependent, and can be modeled mathematically with five parameters. The values of the parameters were determined by optimizing the fit of the model to the data, using a nonlinear regression procedure of a commercial statistical analysis package. Once the parameters of DNA breakage have been determined, absorbed dose can be measured by this technique, which we have termed supercoil relaxation dosimetry. The average accuracy of dose determination for our system over the range of 1–40 Gy was about 5%. Supercoil relaxation dosimetry may be well suited to certain difficult dosimetric problems.

Influence of shape on the accuracy of grid‐based volume computations
View Description Hide DescriptionThe influence of the shape of a region of interest (ROI) on the uncertainty in the sampled volume of the ROI is investigated for computations with regular Cartesian grids. Both mathematically defined volumes and clinically relevant ROIs were studied. The sampling uncertainty is shown to depend on the compactness of the ROI and on effects of grid matching and translational symmetry. In clinical ROIs without translational symmetry the estimate of the sampling uncertainty is improved up to a factor of 2.3 by taking the compactness of the ROI into account. In a spherical ROI grid‐matching effects were demonstrated by means of Fourier transforms. In this type of ROI, grid‐matching effects decrease as well as increase the sampling uncertainty up to a factor of 1.6. Translational symmetry is shown to cause a decrease in the sampling uncertainty convergence power from for spherical ROIs, to for stringlike or for pancakelike cylinders. For clinical ROIs with translational symmetry, similar decreases were found. With the theory derived and these symmetry effects taken into account the experimental uncertainty of volume computation can be estimated for most clinical ROIs within a factor of 2.5. Special care should be taken in grid sampling of volumes inside isodose surfaces of rectangular field techniques. For the volume of a prostate an uncertainty level of 1% or 5% is obtained with less than 1050 or 80 grid points, respectively, while for such an isodose surface up to 16 000 or 500 grid points are required for the same uncertainty levels.

A Monte Carlo model of photon beams used in radiation therapy
View Description Hide DescriptionA generic Monte Carlo model of a photon therapy machine is described. The model, known as McRad, is based on EGS4 and has been in use since 1991. Its primary function has been the characterization of the incident photon fluence for use by dose calculation algorithms. The accuracy of McRad is examined by comparing the dose distributions in a water phantom generated using only the Monte Carlo data with measured dose distributions for two machines in our clinic; a 6 MV Varian Clinac 600C and the 15 MV beam from a Clinac 2100C. The Monte Carlo generated dose distributions are computed using a dose calculation algorithm based on the use of differential pencil beam kernels. It was found that the match to measured data could be improved if the model is tuned by adjusting the energy of the electron beam incident on the target. The beam profiles were found to be more sensitive indicators of the electron beam energy than the depth dose curves. Beyond the depths reached by contaminant electrons, the computed and measured depth dose curves agree to better than 1%. The comparison of beam profiles indicate that in regions up to within 1 cm of the field edge, the measured and computed doses generally agree to within 2%–3%.

Measurement of a photon penumbra‐generating kernel for a convolution‐adapted ratio‐TAR algorithm for 3D treatment planning
View Description Hide DescriptionA method has been developed to measure a photon penumbra‐generating kernel using dosimetry equipment available in most radiation therapy departments. The kernel is used in a convolution‐adapted ratio‐TAR algorithm in our three‐dimensional treatment planning system. The kernel is assumed to be invariant with respect to off‐axis position, axially symmetric, and is divided into short‐ and long‐range components, with a different measurement technique for each. The data required to obtain the short‐range component are measured by scanning across a split‐field geometry incident on a water phantom. The derivative of the measured profile is proportional to one‐dimensional projections across the kernel. Because the kernel is axially symmetric, only one profile measurement is required for each depth. A CT reconstruction technique is used to extract the radial dependence of the kernel from the strip integrals. Electronic noise in the acquisition system yields significant uncertainties in the kernel shape for distances beyond 3 cm. The long‐range portion of the kernel is obtained by examining tissue–air ratios (TARs). The derivative of the TAR at the center of a circular field is proportional to the kernel value at the distance corresponding to the radius of the field. The kernel measurement method was tested by comparing measured and calculated square‐field profiles at a variety of depths. Agreement was within 1% within the field boundary and 3% outside the field boundary for all depths.

Noise reduction by frame averaging: A numerical simulation for portal imaging systems
View Description Hide DescriptionWe have studied the usefulness of both pre‐ and post‐ADC frame summing for the purpose of reducing the effect of quantum noise and digitizationnoise in portal imaging systems. The study is based on the fluorescent‐screen video‐camera type of system. The study predicts the not‐surprising result that provided the noise level at the ADC input is sufficiently large, the overall SNR can be increased by a factor of , where M _{1} and M _{2} are the number of frames summed before and after the ADC. The study also predicts, somewhat unexpectedly, that there is an operating region in which increasing M _{1} actually decreases the SNR in the final image. To avoid this region M _{1}must be less than approximately 6×2^{2B } (1+δ̄^{−1})^{1/2}/(i _{acc} f ), where B is the number of ADC bits, δ̄ is the mean number of optical photons detected by the video camera per detected x‐ray photon,i _{acc} is the open‐field number of detected x‐ray photons per accelerator pulse per pixel, and f is the patient transmission factor. An equivalent statement is that the rms noise at the input to the ADC, σ_{in}, must exceed approximately 0.4qwhere q is the quantization interval of the ADC. It is possible that some systems operate in or close to this region. A second feature of this anomalous behavior is that the final image is not necessarily improved by increasing the number M _{2} of post‐ADC‐summed frames. For example, when σ_{in}/q=0.2, there is no improvement in the overall rms error for M _{2}>32. It is also shown that the standard deviation of the final image is not a suitable indicator of output image quality and that its use can give rise to meaningless results.

Accounting for primary electron scatter in x‐ray beam convolution calculations
View Description Hide DescriptionFermi–Eyges electron‐scattering theory has been incorporated into the primary dose calculation for external x‐ray beam radiotherapy using the convolution method. Incorporating scattering theory into the convolution technique accounts for the density distribution between the interaction and deposition sites, whereas conventional convolution methods only consider the average density between these two points. As the lateral spread of electrons ejected from an interaction site depends on the density distribution, the energy deposition (and hence dose distribution) is predicted more accurately if scattering is accounted for. This new method gives depth dose curves which show better agreement with Monte Carlo calculations in a (slab inhomogeneity) lung phantom than a conventional convolution method, especially at high energies and small field sizes where lateral electronic disequilibrium exists at the central axis. For a 5×5‐cm^{2} 18‐MV beam incident on the lung phantom, a reduction in the maximum error between the convolution and Monte Carlo depth dose curves from 5% to 2.5% is obtained when scattering theory is used in the primary dose calculation. Incorporating scattering theory into the convolution calculation increases the computation time of the primary dose by a factor of 3.

A model for electron‐beam applicator scatter
View Description Hide DescriptionApplicators (or cones), used in conjunction with patient specific cutouts in electron‐beam radiotherapy, may interact with the primary electron beam to produce a secondary beam component (applicator scatter). This component affects machine output as well as the shape of resulting dose distributions. A model has been developed to simulate this scatter component for applicators consisting of trimming plates of arbitrary shape. This model involves sampling established kernels of scatter from edge elements of appropriate materials, obtained through Monte Carlo simulations. The result of the model is a phase space (position, direction, energy, charge, weighting) of applicator scattered particles which can be incorporated into a further Monte Carlo simulation, or as input into another advanced treatment planning algorithm. This model is evaluated by comparison of measured profiles and applicator scatter component depth dose curves with Monte Carlo simulations using simulated phase‐space data as input. Results are very consistent and reveal information on the angular and spatial variation characteristics of this beam component. The results obtained verify the developed model as an accurate predictor of the characteristics of applicator scattered particles.

A Monte Carlo investigation of electron‐beam applicator scatter
View Description Hide DescriptionAn EGS4 Monte Carlo investigation into applicator scatter in clinical electron beams has been undertaken in order to establish the characteristics of electrons incident on the patient surface which have interacted with collimation systems. The applicator scattered component of an electron beam (including that from irregularly shaped cutouts) should be considered when modeling the electron phase space since it represents a component of the beam incident on the patient with widely varying characteristics to those of the primary beam. Scattering off an edge of applicator material is considered in terms of the types and characteristics of incident primary beam, the resulting interactions in the edge, and the fluence and energy characteristics of the emerging particles. Results indicate that the principal component to consider is scattered electrons due to the electron component of the primary beam, and that the fluence and energy characteristics of this component are dependent upon primary beam energy and the configuration of the applicator apertures.

Geometric gradient—A new estimation of the surface normal for three‐dimensional medical imaging
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The nonlinear partial volume effect and computed tomography densitometry of foam and lung
View Description Hide DescriptionA quantitative study was performed to assess the magnitude of the nonlinear partial volume effect (NLPVE) in computed tomography(CT) densitometry of polyethene foam and lung. This effect arises in materials having density variations on the scale of the sampling area of an individual CT‐detector element. It causes a systematic underestimation of the density determined with CT.Foam samples and a resected lung of a goat were imaged with high resolution (20 lp/mm) using a mammography system, and the observed optical density variation in the images was converted into a distribution of pathlengths that x rays penetrate within the solid component of the cellular material. The obtained pathlength distribution was used to calculate the transmission, as seen by a single detector in computed tomography. Comparison with the transmission through homogeneous material of the same thickness gave an estimate of the NLPVE. For the foams studied, the CT‐determined density was found to be too low by approximately 0.3%–0.5% due to this effect. Although these density errors are small, in calibrations of a CT scanner they may be of significance. For lung the underestimation of the density was less than 0.1%. These experimentally derived, NLPVE related CT‐density errors are 32%–84% of those calculated from a simple model of a cellular solid.

Calculation of dose in asymmetric photon fields
View Description Hide DescriptionA method is introduced to calculate monitor units to points off axis. Extensive data are presented comparing this method with measured values of dose per monitor unit on the central ray of asymmetric fields produced by a variety of linear accelerators. The technique demonstrates improvement over existing methods that use large‐field profile data. The method is found to be both simple and accurate: Agreement within ±2% is obtained using parameters readily available within the clinic.

Physical characteristics of a clinical d(48.5)+Be neutron therapy beam produced by a superconducting cyclotron
View Description Hide DescriptionThe Harper Hospital and Wayne State University fast neutron therapy facility is the only one in the world to use a compact superconducting cyclotron and multirod collimator.Neutrons are produced by the interaction of the 48.5‐MeV deuteron beam with a thick internal beryllium target and the compact accelerator is gantry mounted to allow full 360° rotation of the neutron beam about the therapy couch. The deuteron beam strikes the beryllium target at a glancing angle. A flattening filter is used to flatten the asymmetric neutron beam which results from this geometry. Details of the flattening filter design and construction are discussed. The physical characteristics of the resulting neutron therapy beam were measured. The central axis depth‐dose values are approximately equivalent to those of a 4‐MV photon beam. The dose buildup curve reaches its maximum value at a depth of 9 mm in a water phantom and the surface dose is approximately 42%. The beam penumbra produced by the multirod collimator has been measured in terms of the distance between the 20% and 80% isodose lines. The penumbra width for a 10×10‐cm^{2} field at a depth of 10 cm in a water phantom is 1.65±0.1 cm, and is comparable to that achieved with other high‐energy neutron beams. The long‐term stability of the dose monitoring system has been measured and found to be satisfactory. The physical characteristics of the neutron beam are comparable with those of other modern fast neutron therapy facilities.

A simple method of obtaining off‐axis half‐value layers for megavoltage photon beams
View Description Hide DescriptionWe describe a simplified technique for the acquisition of off‐axis beam‐quality data (i.e., half‐value layers in water) for medicallinear accelerators. A measurement protocol is presented in which an ordinary beam‐scanning water phantom is used to accurately position an ionization chamber at appropriate measuring positions. Attenuation coefficients are calculated by performing a regression on the measured data. The technique uses the smallest fields for which lateral electron equilibrium can be established.

Considerations for superficial photon dosimetry
View Description Hide DescriptionDose measurements at superficial energies required special considerations. First, care must be taken in selecting appropriate phantom materials. Materials that are adequate tissue substitutes at megavoltage energies might not be adequate at superficial energies. The suitability of a material can be judged by comparing its mass attenuation and mass energy absorption coefficients at superficial energies to those of the tissue of interest. Second, very low energy x‐ray and electron contaminants must be removed from the superficial beam before they reach the detector. For detectors with a very thin window, this can be achieved by placing thin film on top of the detector. Failure to properly eliminate contaminants can result in a large increase in dose measured directly at the surface.

The evaluation of optimized implants for idealized implant geometries
View Description Hide DescriptionThe purpose of this paper is to investigate the utility of implant quality measures on single stepping‐source brachytherapy treatment plans. Four dwell weight optimization algorithms were applied to four regular geometric implants: single plane, double plane, cuboid, and cylindrical. The dwell weight optimization schemes included equal weighing, two commercial optimization schemes (dose‐point and geometric) and a variation of the Paterson–Parker distribution rules. The implant quality measures were investigated as a function of dose‐per‐integrated reference air kerma (IRAK) to eliminate bias resulting from a prescription choice. A particular dose per IRAK refers to a dose surface that is a function only of the relative dwell weight distribution and is therefore well suited to investigate dwell weight optimization schemes. The implant quality measures included the dose–nonuniformity ratio (DNR) developed by Saw and a coverage index to assess the isodose coverage relative to the implanted volume. These were termed direct quantities due to their clear clinical significance. Additional measures include the ratio of the implant dose–volume histogram (DVH) to that of a point source exhibiting the same IRAK (R _{ p }) and the ratio of the optimized DVH to the equally weighted DVH (EWR). The widths of the R _{ p } curves and depths of the EWR curves were used to characterize these indirect implant quality measures. To evaluate the effectiveness of both the direct and indirect measures, they were correlated with the DNR for an isodose surface that covered the implant (D _{0}). The efficiency of the dwell weight distribution was examined by noting the dose‐per‐IRAK surface D _{0}. The DNR exhibited a distribution with a minimum value in each implant and optimization method. At this point the high‐dose volume is minimized relative to the prescription volume and choosing this dose as a prescription isodose will provide a relatively homogeneous dose distribution. However, the minimum DNR value did not provide a clinically useful implant coverage with most optimization schemes. The exception was the dose‐point optimization that yielded an adequate coverage at the DNR minimum. The EWR curve exhibited a dip (at doseD _{ n }) for most of the optimization schemes which was deepest for the dose‐point optimization. There was no direct correlation between the EWR(D _{ n }) and homogeneity, but a large value of EWR(D _{ n }) consistently predicted a poor homogeneity. An examination of the coverage versus the DNR showed that in all cases, a tradeoff existed between coverage and dose homogeneity. In all cases the dose‐point optimization provided the best compromise between coverage and homogeneity in addition to the most efficient implant. The application of these implant quality measures allowed an examination of the inherent quality of each dwell weight distribution, a task that would be very difficult without this type of guidance. While the indirect quality measures provided some properties that correlated with the direct quality measures, further study is necessary before their role in dose distribution analysis is completely understood. Use of the dose‐per‐IRAK as the independent variable divorced the analysis from an arbitrary prescription criterion.